2023-01-21

Thesis Presentation

In this Markdown presentation, I will present some results of the pilot simulation study that I did for my thesis. My thesis is about efficient audit sample selection. In the pilot simulation study, I compare two methods for efficient sample selection against each other: the sample size approach and the deviance approach. Here follows an overview of some preliminary results.

Results in a table

This table shows the number of iterations and the deviance before and after in the first 100 datasets.

Results in a Figure

Results in an Interactive Figure

The Code to Create the Interactive Figure

library(plotly)

p <- ggplot(aes(x = condition, y = added_units, fill = study), data = total_results) +
  geom_boxplot() +
  theme_classic() + 
  scale_fill_grey() +
  xlab("Condition") +
  ylab("Added Units") +
  theme(legend.title = element_blank(), text = element_text(size = 18),
        axis.text.x = element_text(angle = -30, hjust = 0))

ggplotly(p)

The Problem in an Equation

The minimization procedure can be written as follows: \[min\{\sum_{i,j} \delta_{ij}^+ + \sum_{i,j} \delta_{ij}^-\}\] under constraints \[m_{ij1} = n_{ij1} + \delta_{ij}^+ - \delta_{ij}^-;\] \[m_{ij0} = n_{ij0} - \delta_{ij}^+ + \delta_{ij}^-;\] \[D \leq \chi_{I(J-1)}^2 (1-\alpha);\] \[0 \leq \delta_{ij}^+ \leq n_{ij0};\] \[0 \leq \delta_{ij}^- \leq n_{ij1}.\]

The End